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題名 以SOFR期貨建構利率期限結構：考慮跳躍過程之無套利Nelson-Siegel方法
Constructing Term Structure with SOFR Futures : Arbitrage-Free Nelson-Siegel with Jump-Diffusion Approach
作者 葉宗瑋
Ye, Zong-Wei
貢獻者 林士貴
Lin, Shih-Kuei
葉宗瑋
Ye, Zong-Wei
關鍵詞 SOFR
SOFR 期貨
考慮跳躍過程之 Nelson-Siegel 模型
粒子濾波器
SOFR
SOFR futures
AFNSJ
Particle filter
日期 2022
上傳時間 1-Aug-2022 17:29:52 (UTC+8)
摘要 隨著美元 LIBOR 即將被淘汰，我們迫切需要一個合理的且具有市場代表性的前瞻性期限 SOFR。在本研究中，我們擴展Christensen, Diebold, and Rudebusch (2011) 的方法，提出了考慮跳躍過程之無套利 Nelson-Siegel 模型（arbitrage-free Nelson-Siegel model, AFNSJ）來生成利率期限結構。AFNSJ 模型具有 Nelson-Siegel 架構，以確保對樣本內估計的良好配適度。同時 AFNSJ 模型在理論上也有了重要支持，其滿足資產定價中最重要的理論：無套利條件。此外，AFNSJ 模型藉由通過考慮跳躍過程捕捉 FOMC 會議後短期利率的跳躍。在實證研究中，我們利用粒子濾波器以及加權最大概似估計法來進行估計。其根據均方根誤差和概似比檢驗結果，我們表明AFNSJ 模型在統計上優於沒有跳躍過程的高斯模型。最後，通過研究過濾後的跳躍過程，我們發現 AFNSJ 模型可以廣泛地捕捉到 FOMC 會議和宏觀經濟指示性公告引起的。
With the imminent phased out of USD LIBOR, there is an urgent need for a reasonable and market-representative forward-looking term SOFR. In this study, we propose the arbitrage-free Nelson-Siegel with jump-diffusion model (AFNSJ) extended by Christensen et al. (2011) to generate the interest rate term structure. The AFNSJ model has the Nelson-Siegel framework to ensure a good fit for in-sample estimation. It is also theoretically supported because it satisfies the most crucial theory in asset pricing: the no-arbitrage condition. Furthermore, the AFNSJ model captures the jumps pattern at short rates after the FOMC meeting by considering the jump process. In empirical studies, the particle filter with weighted maximum likelihood estimation was adopted to estimate. The root mean square error and likelihood ratio test results show that the AFNSJ model outperforms the Gaussian model without the jump process statistically. Finally, by investigating the filtered jumps, we find the AFNSJ can extensively capture the shock caused by the FOMC meetings and the announcements of macroeconomic.
參考文獻 Andersen, L. B., & Bang, D. R. (2020). Spike modeling for interest rate derivatives with an application to sofr caplets. Available at SSRN 3700446.

Balduzzi, P., Bertola, G., & Foresi, S. (1997). A model of target changes and the term structure of interest rates. Journal of Monetary Economics, 39(2), 223–249.

Balduzzi, P., Das, S. R., & Foresi, S. (1998). The central tendency: A second factor in bond yields. Review of Economics and Statistics, 80(1), 62–72.

Balduzzi, P., Elton, E. J., & Green, T. C. (2001). Economic news and bond prices: Evidence from the us treasury market. Journal of Financial and Quantitative Analysis, 36(4), 523–
543.

Bernanke, B. S., & Kuttner, K. N. (2005). What explains the stock market’s reaction to federal reserve policy? The Journal of Finance, 60(3), 1221–1257.

Chan, K. F., & Gray, P. (2018). Volatility jumps and macroeconomic news announcements. Journal of Futures Markets, 38(8), 881–897.

Cheridito, P., Filipović, D., & Kimmel, R. L. (2007). Market price of risk specifications for affine models: Theory and evidence. Journal of Financial Economics, 83(1), 123–170.

Christensen, J. H., Diebold, F. X., & Rudebusch, G. D. (2011). The affine arbitrage-free class of nelson–siegel term structure models. Journal of Econometrics, 164(1), 4–20.

Christoffersen, P., Heston, S., & Jacobs, K. (2013). Capturing option anomalies with a variance-dependent pricing kernel. The Review of Financial Studies, 26(8), 1963–2006.

Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica, 53(2), 363–384.

Dai, Q., & Singleton, K. J. (2000). Specification analysis of affine term structure models. The Journal of Finance, 55(5), 1943–1978.

Dai, Q., & Singleton, K. J. (2002). Expectation puzzles, time-varying risk premia, and affine models of the term structure. Journal of Financial Economics, 63(3), 415–441.

Das, S. R. (2002). The surprise element: jumps in interest rates. Journal of Econometrics,106(1), 27–65.

Das, S. R., & Foresi, S. (1996). Exact solutions for bond and option prices with systematic jump risk. Review of Derivatives Research, 1(1), 7–24.

Diebold, F. X., & Li, C. (2006). Forecasting the term structure of government bond yields. Journal of Econometrics, 130(2), 337–364.

Duarte, J. (2004). Evaluating an alternative risk preference in affine term structure models. The Review of Financial Studies, 17(2), 379–404.

Duffee, G. R. (2002). Term premia and interest rate forecasts in affine models. The Journal of Finance, 57(1), 405–443.

Duffie, D., & Kan, R. (1996). A yield-factor model of interest rates. Mathematical Finance, 6(4), 379–406.

Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6), 1343–1376.

Dungey, M., McKenzie, M., & Smith, L. V. (2009). Empirical evidence on jumps in the term structure of the us treasury market. Journal of Empirical Finance, 16(3), 430–445.

Fong, H. G., & Vasicek, O. A. (1991). Fixed-income volatility management. Journal of Portfolio Management, 17(4), 41–46.

Gellert, K., & Schlögl, E. (2021). Short rate dynamics: A fed funds and sofr perspective. FIRN Research Paper.

Green, T. C. (2004). Economic news and the impact of trading on bond prices. The Journal of Finance, 59(3), 1201–1233.

Heitfield, E., & Park, Y.-H. (2019). Inferring term rates from sofr futures prices. Working Paper.

Jarrow, R., Li, H., & Zhao, F. (2007). Interest rate caps “smile”too! but can the libor market models capture the smile? The Journal of Finance, 62(1), 345–382.

Johannes, M. (2004). The statistical and economic role of jumps in continuous-time interest rate models. The Journal of Finance, 59(1), 227–260.

Jones, C. M., Lamont, O., & Lumsdaine, R. L. (1998). Macroeconomic news and bond market volatility. Journal of Financial Economics, 47(3), 315–337.

Litterman, R., & Scheinkman, J. (1991). Common factors affecting bond returns. Journal of Fixed Income, 1(1), 54–61.

Longstaff, F. A., & Schwartz, E. S. (1992). Interest rate volatility and the term structure: A two-factor general equilibrium model. The Journal of Finance, 47(4), 1259–1282.

Lyashenko, A., & Mercurio, F. (2019). Looking forward to backward-looking rates: a modeling framework for term rates replacing libor. Available at SSRN 3330240.

Macrina, A., & Skovmand, D. (2020). Rational savings account models for backward-looking interest rate benchmarks. Risks, 8(1), 23.

Mercurio, F. (2018). A simple multi-curve model for pricing sofr futures and other derivatives. Available at SSRN 3225872.

Nelson, C. R., & Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of Business, 60(4), 473–489.

Pan, J. (2002). The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics, 63(1), 3–50.

Santa-Clara, P., & Yan, S. (2010). Crashes, volatility, and the equity premium: Lessons from s&p 500 options. The Review of Economics and Statistics, 92(2), 435–451.

Savor, P., & Wilson, M. (2014). Asset pricing: A tale of two days. Journal of Financial Economics, 113(2), 171–201.

Skov, J. B., & Skovmand, D. (2021). Dynamic term structure models for sofr futures. Journal of Futures Markets, 41(10), 1520–1544.

Svensson, L. E. (1994). Estimating and interpreting forward interest rates: Sweden 1992-1994.Working Paper.

Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.

Wright, J. H., & Zhou, H. (2009). Bond risk premia and realized jump risk. Journal of Banking & Finance, 33(12), 2333–2345
描述 碩士
國立政治大學
金融學系
109352026
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109352026
資料類型 thesis
dc.contributor.advisor 林士貴zh_TW
dc.contributor.advisor Lin, Shih-Kueien_US
dc.contributor.author (Authors) 葉宗瑋zh_TW
dc.contributor.author (Authors) Ye, Zong-Weien_US
dc.creator (作者) 葉宗瑋zh_TW
dc.creator (作者) Ye, Zong-Weien_US
dc.date (日期) 2022en_US
dc.date.accessioned 1-Aug-2022 17:29:52 (UTC+8)-
dc.date.available 1-Aug-2022 17:29:52 (UTC+8)-
dc.date.issued (上傳時間) 1-Aug-2022 17:29:52 (UTC+8)-
dc.identifier (Other Identifiers) G0109352026en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141065-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融學系zh_TW
dc.description (描述) 109352026zh_TW
dc.description.abstract (摘要) 隨著美元 LIBOR 即將被淘汰，我們迫切需要一個合理的且具有市場代表性的前瞻性期限 SOFR。在本研究中，我們擴展Christensen, Diebold, and Rudebusch (2011) 的方法，提出了考慮跳躍過程之無套利 Nelson-Siegel 模型（arbitrage-free Nelson-Siegel model, AFNSJ）來生成利率期限結構。AFNSJ 模型具有 Nelson-Siegel 架構，以確保對樣本內估計的良好配適度。同時 AFNSJ 模型在理論上也有了重要支持，其滿足資產定價中最重要的理論：無套利條件。此外，AFNSJ 模型藉由通過考慮跳躍過程捕捉 FOMC 會議後短期利率的跳躍。在實證研究中，我們利用粒子濾波器以及加權最大概似估計法來進行估計。其根據均方根誤差和概似比檢驗結果，我們表明AFNSJ 模型在統計上優於沒有跳躍過程的高斯模型。最後，通過研究過濾後的跳躍過程，我們發現 AFNSJ 模型可以廣泛地捕捉到 FOMC 會議和宏觀經濟指示性公告引起的。zh_TW
dc.description.abstract (摘要) With the imminent phased out of USD LIBOR, there is an urgent need for a reasonable and market-representative forward-looking term SOFR. In this study, we propose the arbitrage-free Nelson-Siegel with jump-diffusion model (AFNSJ) extended by Christensen et al. (2011) to generate the interest rate term structure. The AFNSJ model has the Nelson-Siegel framework to ensure a good fit for in-sample estimation. It is also theoretically supported because it satisfies the most crucial theory in asset pricing: the no-arbitrage condition. Furthermore, the AFNSJ model captures the jumps pattern at short rates after the FOMC meeting by considering the jump process. In empirical studies, the particle filter with weighted maximum likelihood estimation was adopted to estimate. The root mean square error and likelihood ratio test results show that the AFNSJ model outperforms the Gaussian model without the jump process statistically. Finally, by investigating the filtered jumps, we find the AFNSJ can extensively capture the shock caused by the FOMC meetings and the announcements of macroeconomic.en_US
dc.description.tableofcontents 摘要 i
Abstract ii
Contents iii
List of Figures v
List of Tables vi
1 Introduction 1
2 Literature Review 7
2.1 Term Structure Models 7
2.2 Term SOFR 8
3 Methodologies 10
3.1 Nelson-Siegel Framework 10
3.1.1 Nelson-Siegel Model 10
3.1.2 Dynamic Nelson-Siegel Model 11
3.1.3 Arbitrage-Free Nelson-Siegel Model 12
3.1.4 Arbitrage-Free Nelson-Siegel with Jump-Diffusion Model 15
3.2 Pricing SOFR Futures 17
3.2.1 One-Month SOFR Futures 18
3.2.2 Three-Month SOFR Futures 19
3.3 Particle Filter 19
4 Empirical Results 24
4.1 Data Description 24
4.2 Parameters Estimation 25
4.3 Model Performance 26
4.4 Term SOFR 31
4.5 Macroeconomic Announcements 34
5 Conclusion and Future Work 37
5.1 Conclusions 37
5.2 Future Works 38
References 39
Appendices 43		zh_TW
dc.format.extent 1093560 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109352026en_US
dc.subject (關鍵詞) SOFRzh_TW
dc.subject (關鍵詞) SOFR 期貨zh_TW
dc.subject (關鍵詞) 考慮跳躍過程之 Nelson-Siegel 模型zh_TW
dc.subject (關鍵詞) 粒子濾波器zh_TW
dc.subject (關鍵詞) SOFRen_US
dc.subject (關鍵詞) SOFR futuresen_US
dc.subject (關鍵詞) AFNSJen_US
dc.subject (關鍵詞) Particle filteren_US
dc.title (題名) 以SOFR期貨建構利率期限結構：考慮跳躍過程之無套利Nelson-Siegel方法zh_TW
dc.title (題名) Constructing Term Structure with SOFR Futures : Arbitrage-Free Nelson-Siegel with Jump-Diffusion Approachen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Andersen, L. B., & Bang, D. R. (2020). Spike modeling for interest rate derivatives with an application to sofr caplets. Available at SSRN 3700446.

Balduzzi, P., Bertola, G., & Foresi, S. (1997). A model of target changes and the term structure of interest rates. Journal of Monetary Economics, 39(2), 223–249.

Balduzzi, P., Das, S. R., & Foresi, S. (1998). The central tendency: A second factor in bond yields. Review of Economics and Statistics, 80(1), 62–72.

Balduzzi, P., Elton, E. J., & Green, T. C. (2001). Economic news and bond prices: Evidence from the us treasury market. Journal of Financial and Quantitative Analysis, 36(4), 523–
543.

Bernanke, B. S., & Kuttner, K. N. (2005). What explains the stock market’s reaction to federal reserve policy? The Journal of Finance, 60(3), 1221–1257.

Chan, K. F., & Gray, P. (2018). Volatility jumps and macroeconomic news announcements. Journal of Futures Markets, 38(8), 881–897.

Cheridito, P., Filipović, D., & Kimmel, R. L. (2007). Market price of risk specifications for affine models: Theory and evidence. Journal of Financial Economics, 83(1), 123–170.

Christensen, J. H., Diebold, F. X., & Rudebusch, G. D. (2011). The affine arbitrage-free class of nelson–siegel term structure models. Journal of Econometrics, 164(1), 4–20.

Christoffersen, P., Heston, S., & Jacobs, K. (2013). Capturing option anomalies with a variance-dependent pricing kernel. The Review of Financial Studies, 26(8), 1963–2006.

Cox, J. C., Ingersoll Jr, J. E., & Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica, 53(2), 363–384.

Dai, Q., & Singleton, K. J. (2000). Specification analysis of affine term structure models. The Journal of Finance, 55(5), 1943–1978.

Dai, Q., & Singleton, K. J. (2002). Expectation puzzles, time-varying risk premia, and affine models of the term structure. Journal of Financial Economics, 63(3), 415–441.

Das, S. R. (2002). The surprise element: jumps in interest rates. Journal of Econometrics,106(1), 27–65.

Das, S. R., & Foresi, S. (1996). Exact solutions for bond and option prices with systematic jump risk. Review of Derivatives Research, 1(1), 7–24.

Diebold, F. X., & Li, C. (2006). Forecasting the term structure of government bond yields. Journal of Econometrics, 130(2), 337–364.

Duarte, J. (2004). Evaluating an alternative risk preference in affine term structure models. The Review of Financial Studies, 17(2), 379–404.

Duffee, G. R. (2002). Term premia and interest rate forecasts in affine models. The Journal of Finance, 57(1), 405–443.

Duffie, D., & Kan, R. (1996). A yield-factor model of interest rates. Mathematical Finance, 6(4), 379–406.

Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6), 1343–1376.

Dungey, M., McKenzie, M., & Smith, L. V. (2009). Empirical evidence on jumps in the term structure of the us treasury market. Journal of Empirical Finance, 16(3), 430–445.

Fong, H. G., & Vasicek, O. A. (1991). Fixed-income volatility management. Journal of Portfolio Management, 17(4), 41–46.

Gellert, K., & Schlögl, E. (2021). Short rate dynamics: A fed funds and sofr perspective. FIRN Research Paper.

Green, T. C. (2004). Economic news and the impact of trading on bond prices. The Journal of Finance, 59(3), 1201–1233.

Heitfield, E., & Park, Y.-H. (2019). Inferring term rates from sofr futures prices. Working Paper.

Jarrow, R., Li, H., & Zhao, F. (2007). Interest rate caps “smile”too! but can the libor market models capture the smile? The Journal of Finance, 62(1), 345–382.

Johannes, M. (2004). The statistical and economic role of jumps in continuous-time interest rate models. The Journal of Finance, 59(1), 227–260.

Jones, C. M., Lamont, O., & Lumsdaine, R. L. (1998). Macroeconomic news and bond market volatility. Journal of Financial Economics, 47(3), 315–337.

Litterman, R., & Scheinkman, J. (1991). Common factors affecting bond returns. Journal of Fixed Income, 1(1), 54–61.

Longstaff, F. A., & Schwartz, E. S. (1992). Interest rate volatility and the term structure: A two-factor general equilibrium model. The Journal of Finance, 47(4), 1259–1282.

Lyashenko, A., & Mercurio, F. (2019). Looking forward to backward-looking rates: a modeling framework for term rates replacing libor. Available at SSRN 3330240.

Macrina, A., & Skovmand, D. (2020). Rational savings account models for backward-looking interest rate benchmarks. Risks, 8(1), 23.

Mercurio, F. (2018). A simple multi-curve model for pricing sofr futures and other derivatives. Available at SSRN 3225872.

Nelson, C. R., & Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of Business, 60(4), 473–489.

Pan, J. (2002). The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics, 63(1), 3–50.

Santa-Clara, P., & Yan, S. (2010). Crashes, volatility, and the equity premium: Lessons from s&p 500 options. The Review of Economics and Statistics, 92(2), 435–451.

Savor, P., & Wilson, M. (2014). Asset pricing: A tale of two days. Journal of Financial Economics, 113(2), 171–201.

Skov, J. B., & Skovmand, D. (2021). Dynamic term structure models for sofr futures. Journal of Futures Markets, 41(10), 1520–1544.

Svensson, L. E. (1994). Estimating and interpreting forward interest rates: Sweden 1992-1994.Working Paper.

Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.

Wright, J. H., & Zhou, H. (2009). Bond risk premia and realized jump risk. Journal of Banking & Finance, 33(12), 2333–2345		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202200930en_US